New periodic solutions for the circular restricted 3-body and 4-body problems

Qunyao Yin; Shiqing Zhang

doi:10.3934/cpaa.2010.9.249

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2010, Volume 9, Issue 1: 249-260. Doi: 10.3934/cpaa.2010.9.249

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New periodic solutions for the circular restricted 3-body and 4-body problems

Qunyao Yin¹ and
Shiqing Zhang²

1.
College of Chengxian, Dongnan University, Nanjing 210088
2.
College of Mathematics, Sichuan University, Chengdu 610064

Received: June 30, 2008

Revised: May 31, 2009

Published: December 2009

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Abstract

For the circular restricted 3-body and 4-Body problems in $\mathbb{R}^2$, we prove the existence of new symmetric noncollision periodic solutions with some fixed winding numbers and masses.

Keywords:

Circular restricted 3(or 4)-body problem,
noncollision periodic solutions,
variational methods.

Mathematics Subject Classification: Primary: 70G75, 70F07, 70F10; Secondary: 70F15.

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